CHAPTER 5 SIMULATION RESULTS & DISCUSSION …shodhganga.inflibnet.ac.in/bitstream/10603/4566/15/15_chapter 5.pdf · CHAPTER – 5 SIMULATION RESULTS & DISCUSSION 5.0 INTRODUCTION

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CHAPTER – 5

SIMULATION RESULTS & DISCUSSION

5.0 INTRODUCTION

This chapter deals with testing of GSHDC algorithm for IEEE

test systems. The standard IEEE 14, 30 and 57 systems are

considered to investigate the effectiveness of the proposed

methodology. The test is carried with a 1.4-GHz Pentium-IV PC. The

GSHDC has been developed by the use of MATLAB version 7. The

simulation results are compared with other popular methodologies in

judicious way.

GSHDC Method is implemented for two Test cases:

Test-1: Suboptimal Solution obtained through IP method

Test-2: Suboptimal Solution obtained through PSO method

Suboptimal solution is obtained for two individual objectives and

one Multi-objective:

Objective-1: Minimum Fuel Cost

Objective-2: Minimum Power Loss

Using the OPF solutions obtained through objective-1 &2 as

parent chromosomes, population is generated for the multi-objective

OPF problem. This is referred as:

Objective-3: Multi-Objective

GSHDC is implemented for each Test case and each objective for

three case studies that is, three IEEE Test systems.

Case-1: IEEE 14-Bus System

189



In addition to above two tests, GSHDC is also implemented with

suboptimal solution obtained through modified penalty factor method

to test its effectiveness. This case is referred as Test-3.

Simulation Test results are presented as per the following tree

diagram shown in the Fig.5.1

Tree diagram can be read as follows:

Example:

1) Test-1, Objective-1, Case-1 indicates the GSHDC results for IEEE

14-Bus System for minimum fuel cost using OPF suboptimal

solution based on IP Method.

Fig: 5.1 Tree Diagram indicating various simulation test results

OPF- Simulation Test Results

Test-3: OPF suboptimal Solution Using

modified penalty factor method

TEST-1

OPF suboptimal Solution Using IP Method

Objective-1

GSHDC solution for minimum power loss Case-1: 14- Bus System

Case-2: 30- Bus System


Objective-2 GSHDC solution for minimum fuel cost




Objective-3 GSHDC-MOGA

Multi-Objective solution for minimum fuel cost & minimum power loss

Case-1: 14- Bus System Case-2: 30- Bus System Case-3: 57- Bus System

TEST-2 OPF suboptimal Solution Using PSO Method

Objective-1

GSHDC solution for minimum power loss Case-1: 14- Bus System



Objective-2 GSHDC solution for minimum fuel cost




Objective-3 GSHDC-MOGA

Multi-Objective solution for minimum fuel cost & minimum power loss

Case-1: 14- Bus System Case-2: 30- Bus System Case-3: 57- Bus System

190

2) Test-1, Objective-2, Case-3 indicates the GSHDC results for IEEE

57-Bus System for minimum power loss using OPF suboptimal

solution based on IP Method.

3) Test-2, Objective-3, Case-1 indicates the multi objective GSHDC-

MOGA results for IEEE 14-Bus System where the OPF for

minimum fuel cost and power loss using suboptimal solution

based on PSO Method.

5.1 OPF SIMULATION RESULTS - IEEE 14 BUS TEST SYSTEM

In this study, the standard IEEE 14-Bus 5 Generator test

system is considered to investigate effectiveness of the GSHDC

approach. The IEEE 14-bus system has 20 transmission lines. The

single line diagram is shown in Fig.5.2. The values of fuel cost

coefficients are given in Table 5.1. The total load demand of the

system is 259 MW and 5 -Generators should share load optimally.

Fig: 5.2 IEEE 14 – Bus Test System [101]

191

Table 5.2: Generator Operating Limits

Minimum or Maximum Generation

limits of Generators are presented

in Table 5.2.

Parameter values for GA are presented in Table 5.3

Table 5.3: Parameter values Genetic Algorithm

5.1.1 Test-1 Objective-1 case-1

Testing of GSHDC Algorithm for OPF Solution using suboptimal

solution obtained by Interior Point Method-Minimum Fuel Cost

For the IEEE 14 Bus Test system initially, an OPF solution is

obtained by using IP method. Taking this as suboptimal solution, a

high density cluster for minimum fuel cost is formed in the vicinity of

suboptimal solution by GSHDC Algorithm. Finally with the help of a

well defined fitness function genetic search is carried out to find the

optimal solution. The results are furnished for the objective namely,

minimum cost. The test results include the total cost of generation,

generation schedule, generator bus voltage magnitudes and CPU

Table 5.1: Generator Fuel Cost Coefficients

Sl.No Generator at bus #

i ($/h) i ($/MWhr) i ($/MWhr2)

1 1 0 20 0.0430293

2 2 0 20 0.25

3 3 0 40 0.01

4 6 0 40 0.01

5 8 0 40 0.01


PGiMn (MW)

PGiMax

(MW)

1 1 0 332.4

2 2 0 140

3 3 0 100

4 6 0 100

5 8 0 100

Population Size 100 Mutation Probability 0.01

No. of Generations 300 Crossover Probability 0.08

192

execution time. Table 5.4 provides generation schedule, cost of

generation and CPU time for the minimum fuel cost objective.

Table 5.5 provides bus voltage magnitudes for the minimum fuel cost

objective. From Table 5.4, it can be seen both cost of generation and

CPU execution time in GSHDC method as compared IP method are

superior.

Table 5.4 OPF Solution for IEEE 14-Bus System

Test-1 Objective-1 Case-1 (Generation Schedule, cost, CPU time)

Table 5.5 OPF Solution for IEEE 14-Bus System-Test-1 Objective-

1 Case-1 (Generator Bus Voltage Magnitude, power loss)

From Table 5.5, it can be seen bus voltage magnitudes at

generator buses are improved in GSHDC method. Also, the power loss

in transmission system is found to be less as compared to IP method.

Parameter Suboptimal OPF solution by IP Method

GSHDC-IP Method

PG1 (MW) 194.33 195.01

PG2 (MW) 36.72 39.45

PG3 (MW) 28.74 27.94

PG6(MW) 11.20 9.20

PG8 (MW) 8.50 7.84

Total Cost of Generation

8081.53 $/h 8043.30 $/h

CPU execution time 1.75 seconds 1.43 seconds

Parameter Suboptimal OPF solution by IP

Method GSHDC-IP Method

VG1 1.06 1.06

VG2 1.041 1.045

VG3 1.01 1.016

VG6 1.06 1.07

VG8 1.06 1.09

Power loss (MW) 9.287 9.2523

193


Testing of GSHDC Algorithm for OPF Solution using suboptimal solution

obtained by Interior Point Method-Minimum Power loss

For the IEEE 14 Bus Test system initially, an OPF solution for

minimum power loss is obtained by using IP method. Taking this as

suboptimal solution, a high density cluster for minimum power loss in

the vicinity of suboptimal solution is formed. Finally with the help of

a well defined fitness function for minimum power loss, a genetic

search is carried out to find the optimal solution. The results are

furnished for the objective namely, minimum power loss. The test

results include the total cost of generation, generation schedule,

generator bus voltage magnitudes and CPU execution time. Table 5.6

provides generation schedule, cost of generation and CPU time for the

minimum power loss objective. Table 5.7 provides bus voltage

magnitudes for the minimum power loss objective.



From Table 5.6, it can be seen both cost of generation and CPU

execution time in GSHDC method as compared IP method are

superior.

Parameter Suboptimal OPF solution by

IP Method GSHDC-IP Method

PG1 (MW) 194.32 193.49

PG2 (MW) 40.27 40.20

PG3 (MW) 27.85 28.86

PG6(MW) 10.73 10.66

PG8 (MW) 6.28 6.15


8082.77 $/h 8043.80 $/h


194

Table 5.7 OPF Solution for IEEE 14-Bus System - Test-1

Objective-2 Case-1 (Generator Bus Voltage Magnitude, power loss)




Comparison of Bus voltage magnitudes in both the methods indicates

that there is no significant difference.


Testing of MOGA-GSHDC Algorithm for OPF Solution, using two

high density core points of two individual high density clusters for

minimum fuel cost and minimum Power loss,

Now, for the IEEE 14 Bus Test system, a multi objective OPF

solution is obtained using core points available in two high density

clusters that is, for minimum fuel cost and minimum power loss by

using IP method. Table 5.8 (a) provides member ship function values

of the non-dominant OPF solutions which are the core points of each

of high density clusters.


IP Method GSHDC-IP Method

VG1 1.06 1.06

VG2 1.045 1.047

VG3 1.01 1.010

VG6 1.07 1.072

VG8 1.09 1.09

Power loss (MW) 9.2469 9.1643

195

Table 5.8 (a) OPF Solution for IEEE 14-Bus System - Test-1

Objective-3 Case-1

f1,max=8063.70 f1,min = 8043.30 f2,max = 9.5041 f2,min = 9.1645

f1,max - f1,min = 20.40

f2,max - f2,min = 0.3396

Membership function Values: Membership function values for the items

in 2nd row are calculated as per the following.

μ1 = (8063.70- 8043.60)/ 20.40 = 0.9852

μ2 = (9.5041 - 9.3725)/ 0.3396 = 0.3875

∑ μ1 +∑ μ2 = 8.1591 + 7.363=15.5221

μD = (0.9852+ 0.3875) / (15.5221) = 0.08843

Multi-Objective OPF Solution-Decision Making

From the Table 5.8, it is observed the μD has maximum value in

7th row. Accordingly the corresponding values of f1 and f2 are taken as

the multi objective OPF solution for the objectives minimum fuel cost

and minimum power loss respectively.

Minimum Fuel Cost Minimum Power Loss

Sl. No.

Total fuel cost for

minimum generation

cost

Member ship

function value

Total fuel cost for

minimum power loss

Member ship

function value

Decision making

f1 μ1 f2 μ2 μD

01 8043.30 1.0 9.3706 0.3931 0.08974

02 8043.60 0.9852 9.3725 0.3875 0.08843

03 8043.80 0.9754 9.5041 0.0 0.06167

04 8044.10 0.9607 9.2523 0.7414 0.10965

05 8044.40 0.9460 9.2737 0.6784 0.10465

06 8045.10 0.9117 9.3039 0.5895 0.09671

07 8046.35 0.8504 9.1900 0.9249 0.11437

08 8047.23 0.8073 9.2069 0.9010 0.11005

09 8055.43 0.4053 9.2469 0.7573 0.07489

10 8057.23 0.3171 9.1645 1.0 0.08485

11 8063.70 0.0 9.1679 0.9899 0.06377

8.1591 7.363

196

The values of f1 and f2 are:

f1 - Minimum Fuel Cost: 8046.35 $/h.

f2 - Minimum Power Loss - 9.1900 MW.

Table 5.8 (b) provides generation schedule, cost of generation and

CPU time, bus voltage magnitudes for the MOGA-IP OPF solution for

IEEE 14- Bus System.

Table 5.8 (b) OPF Solution for IEEE 14-Bus System - Test-1

Objective-3 Case-1


Testing of GSHDC-PSO Algorithm for OPF Solution using suboptimal

solution obtained by Particle Swarm Optimization Method


obtained by using PSO method. Taking this as suboptimal solution, a


suboptimal solution by GSHDC-PSO Algorithm. Finally with the help

of a well defined fitness function genetic search is carried out to find

the optimal solution. The results are furnished for the objective

namely, minimum cost. The test results include the total cost of

generation, generation schedule, generator bus voltage magnitudes

and CPU execution time. Table 5.9 provides generation schedule, cost

Parameter MOGA-IP OPF Result Parameter MOGA-IP OPF Result

PG1 (MW) 195.49 VG1 1.06

PG2 (MW) 40.70 VG2 1.023

PG3 (MW) 29.29 VG3 1.02

PG6(MW) 11.22 VG6 1.072

PG8 (MW) 5.83 VG8 1.09


8046.35 $/h Power loss (MW)

9.1900 CPU execution

time 1.83 seconds

197

of generation and CPU time for the min. cost objective. Table 5.10

provides bus voltage magnitudes for the min. cost objective.


execution time in GSHDC method as compared PSO method are

superior. From Table 5.10, it can be seen bus voltage magnitudes at


in transmission system is found to be less as compared to PSO

method.




Testing of GSHDC Algorithm for OPF Solution using suboptimal solution

obtained by Interior Point Method-Minimum Power loss



Parameter Suboptimal OPF solution by PSO Method

GSHDC-PSO Method

PG1 (MW) 195.45 193.36

PG2 (MW) 36.93 40.86

PG3 (MW) 29.51 25.51

PG6(MW) 6.64 7.99

PG8 (MW) 11.06 10.67

Total Cost of Generation 8079.40 $/h 8038.80 $/h



GSHDC-PSO Method

VG1 1.06 1.06

VG2 1.042 1.045

VG3 1.012 1.018

VG6 1.05 1.09

VG8 1.062 1.09

Power loss (MW) 9.257 9.1995

198












magnitudes for the minimum power loss objective. From Table 5.11, it

can be seen both cost of generation and CPU execution time in

GSHDC method as compared PSO method are superior.




PSO Method GSHDC-PSO Method

PG1 (MW) 195.32 193.35

PG2 (MW) 39.27 39.80

PG3 (MW) 28.85 27.86

PG6(MW) 09.73 11.66

PG8 (MW) 5.28 5.80

Total Cost of Generation 8072.77 $/h 8042.10 $/h


199


Objective-2 Case-1(Generator Bus Voltage Magnitude, power loss)




method. Comparison of Bus voltage magnitudes in both the methods

indicates that there is no significant difference.




minimum fuel cost and minimum Power loss.




using PSO method. Table 5.13 (a) provides member ship function

values of the non-dominant OPF solutions which are the core points of

each of high density clusters.


GSHDC-PSO Method

VG1 1.06 1.06

VG2 1.05 1.047

VG3 1.02 1.010

VG6 1.065 1.072

VG8 1.09 1.09

Power loss (MW) 9.2567 9.1587

200


Objective-3 Case-1


Sl. No.

Total fuel cost for minimum

generation cost

Member ship

function value

Total Power loss

Member ship

function value

Decision making

f1 μ1 f2 μ2 μD

01 8038.80 1.0 9.3506 0.2212 0.08472

02 8039.60 0.9282 9.3625 0.1729 0.0764

03 8041.80 0.8564 9.4051 0.0 0.059418

04 8042.10 0.8421 9.2423 0.6607 0.093049

05 8042.40 0.8277 9.2747 0.5292 0.08518

06 8043.10 0.7942 9.3139 0.3701 0.075918

07 8044.35 0.7344 9.1800 0.9131 0.114307

08 8046.23 0.6445 9.1881 0.8807 0.10582

09 8048.13 0.5536 9.1981 0.8044 0.09422

10 8053.42 0.3004 9.1587 1.0 0.08987

11 8059.70 0.0 9.1609 0.9910 0.06268

7.4815 6.9308


f1,max - f1,min = 20.90 f2,max - f2,min = 0.2464

Membership function Values: Membership function values for 2nd row

are calculated as per the following.

μ1 = (8059.70- 8039.60)/ 20.90 = 0.9282

μ2 = (9.4051- 9.3625)/ 0.2464= 0.1729

μD = (0.9282+ 0.1729) / (7.4815+ 6.9308) = 0.0764


From the Table 5.13, it is observed the μD has maximum value

in 7th row. Accordingly the corresponding values of f1 and f2 are taken

as the multi objective OPF solution for the objectives minimum fuel

cost and minimum power loss respectively.




201


Objective-3 Case-1

Table 5.13 (b) provides generation schedule, cost of generation

and CPU time, bus voltage magnitudes for the MOGA-PSO OPF

solution for IEEE 14- Bus System. MOGA-PSO results when compared

to MOGA-IP results, it can be seen OPF results are better through

former method.

5.2 OPF SIMULATION RESULTS - IEEE 30 BUS TEST SYSTEM




single line diagram is shown in Fig.5.2. The total load demand of the

system is 283.40 MW and 6 -Generators should share load optimally.

The values of fuel cost coefficients are given in Table 5.14. Minimum

or Maximum Generation limits of Generators are presented in

Table 5.15. The parameters values for GA are parented in Table: 5.16

Parameter MOGA-PSO OPF Result


PG1 (MW) 194.49 VG1 1.06

PG2 (MW) 41.70 VG2 1.043

PG3 (MW) 29.89 VG3 1.015

PG6(MW) 12.00 VG6 1.042

PG8 (MW) 5.12 VG8 1.012


8044.35 $/h Power loss (MW)

9.1800 CPU execution

time 1.92 seconds

202

Fig 5.3 IEEE 30-Bus Test System [101]




i ($/h) I ($/MWhr) i ($/MWhr2)

1 1 0 2.0 0.02

2 2 0 1.75 0.0175

3 5 0 1.0 0.0625

4 8 0 3.25 0.0083

5 11 0 3.0 0.025

6 13 0 3.0 0.025


PGiMn (MW) PGiMax(MW)

1 1 50 200

2 2 20 80

3 5 15 50

4 8 10 35

5 11 10 30

6 13 12 40




203



solution obtained by Interior Point Method-Minimum Fuel Cost.










generation and CPU time for the min. cost objective. Table 5.18







GSHDC-IP Method

PG1 (MW) 175.76 175.42

PG2 (MW) 48.81 48.85

PG5 (MW) 21.54 21.71

PG8(MW) 24.71 23.68

PG11 (MW) 12.35 12.71

PG13 (MW) 12 11.62

Total Cost of Generation 810.61 $/h 806.7008


Parameter Suboptimal OPF solution by IP Method GSHDC-IP Method

VG1 1.019 1.05

VG2 1.03 1.041

VG5 1.00 1.013

VG8 1.00 1.07

VG11 1.00 1.09

VG13 1.00 1.02

power loss (MW)

11.43 10.5920

204


execution time in GSHDC method as compared IP method are






solution obtained by Interior Point Method-Minimum Power loss.













205


execution time in GSHDC method as compared to IP method are




Comparison of Bus voltage magnitudes in both the methods indicates

that there is no significant difference.








GSHDC-IP Method

PG1 (MW) 175.43 175.44

PG2 (MW) 47.81 48.86

PG5 (MW) 25.54 23.10

PG8(MW) 25.71 23.67

PG11 (MW) 12.56 11.56

PG13 (MW) 12 11.32


812.00 $/h 806.8495

CPU execution time 3.54 seconds 2.74




GSHDC-IP Method

VG1 1.012 1.019

VG2 1.000 1.000

VG5 1.000 1.000

VG8 1.000 1.000

VG11 1.000 1.000

VG13 1.000 1.000

power loss (MW) 10.830 10.558

206




using IP method. Table 5.21(a) provides member ship function values

of the non-dominant OPF solutions which are the core points of each

of high density clusters.

f1,max=806.8495 f1,min =806.7008 f2,max =10.7330 f2,min = 10.5580




μ1 = (806.8495- 806.7031)/ 0.1487 = 0.9845

μ2 = (10.7330- 10.7109)/ 0.1750= 0.1262

∑ μ1 + ∑ μ2 =7.4636+5.675 =13.1386

μD = (0. 9845+0.12620)/( 13.1386) = 0.08453


Objective-3 Case-2


Sl. No.

Total fuel cost for minimum generation

cost

Member ship function

value

Total Power loss

Member ship function value

Decision making

f1 μ1 f2 μ2 μD

01 806.7008 1.0 10.6934 0.2262 0.093332

02 806.7031 0.9845 10.7109 0.1262 0.084537

03 806.7073 0.9562 10.7330 0.0 0.072777

04 806.7135 0.9145 10.6296 0.5908 0.114570

05 806.7228 0.8520 10.6301 0.5880 0.109600

06 806.7289 0.8110 10.6571 0.4337 0.094736

07 806.7332 0.7821 10.6157 0.6702 0.110536

08 806.7555 0.6321 10.6226 0.6308 0.096121

09 806.7860 0.4270 10.6274 0.6034 0.076425

10 806.8340 0.1042 10.5580 1.0 0.084044

11 806.8495 0.0 10.5920 0.8057 0.061323

∑ μ1 =7.4636 ∑ μ2=5.675

207


From the Table 5.21, it is observed the μD has maximum value

in 4th row. Accordingly the corresponding values of f1 and f2 are taken

as the multi objective OPF solution for the objectives minimum fuel

cost and minimum power loss respectively.



f2 - Minimum Power Loss- 10.6296 MW.


and CPU time, bus voltage magnitudes for the MOGA-IP OPF solution

for IEEE 14- Bus System.


Objective-3 Case-2









Parameter MOGA-IP OPF Result

Parameter MOGA-IP OPF Result

PG1 (MW) 176.43 VG1 1.019

PG2 (MW) 48.81 VG2 1.020

PG5 (MW) 25.54 VG3 1.003

PG8(MW) 23.71 VG6 1.023

PG11 (MW) 11.56 VG8 1.011

PG13 (MW) 12.00 VG9 1.000

Total Cost of Generation 806.7135 Power loss (MW)

10.6296

CPU execution time 3.1 sec

208



generation and CPU time for the min. cost objective. Table 5.23





execution time in GSHDC method as compared to PSO method are

superior.






method.


GSHDC-PSO Method

PG1 (MW) 167.76 150.45

PG2 (MW) 47.77 59.28

PG5 (MW) 22.54 23.11

PG8(MW) 23.71 30.20

PG11 (MW) 14.56 15.00

PG13 (MW) 12 14.08

Total Cost of Generation 807.961 $/h 798.9925

CPU execution time 3.57 seconds 2.54 sec

Parameter Suboptimal OPF solution by PSO

Method GSHDC-PSO

Method

VG1 1.02 1.016

VG2 1.04 1.000

VG5 1.00 1.000

VG8 1.00 1.000

VG11 1.00 1.000

VG13 1.00 1.000

Power loss (MW) 11.11 8.7190

209



solution obtained by Interior Point Method-Minimum Power loss.


minimum power loss is obtained by using PSO method. Taking this

as suboptimal solution, a high density cluster for minimum power loss

in the vicinity of suboptimal solution is formed. Finally with the help

of a well defined fitness function for minimum power loss, a genetic









Objective-2 Case-2 (Generation Schedule, cost, CPU time)


execution time in GSHDC method as compared PSO method are

superior.


PSO Method GSHDC-PSO Method

PG1 (MW) 174.20 150.18

PG2 (MW) 47.90 58.80

PG5 (MW) 24.44 23.17

PG8(MW) 26.12 31.62

PG11 (MW) 13.27 14.76

PG13 (MW) 12 13.53


807.56 $/h 799.1345

CPU execution time 3.12 seconds 2.76 sec

210







Objective-3 Case-2


Objective-2 Case-2 (Generator Bus Voltage Magnitude,

power loss)


GSHDC-PSO Method

VG1 1.022 1.016

VG2 1.034 1.000

VG5 1.00 1.000

VG8 1.00 1.000

VG11 1.00 1.000

VG13 1.00 1.000

Power loss (MW) 10.47 8.6699


Sl. No.

Total fuel cost for minimum generation cost


Total Power loss


Decision making

f1 μ1 f2 μ2 μD

01 798.9925 1.0000 8.7190 0.0924 0.10688

02 798.9951 0.9579 8.7223 0.0314 0.09679

03 799.0021 0.8446 8.7240 0.0000 0.08264

04 799.0044 0.8074 8.7184 0.1035 0.08912

05 799.0066 0.7718 8.7185 0.1016 0.08545

06 799.0076 0.7556 8.7189 0.0942 0.08315

07 799.0089 0.7346 8.7090 0.2741 0.09869

08 799.0100 0.7168 8.7113 0.2347 0.09310

09 799.0138 0.6553 8.7175 0.1201 0.07587

10 799.0171 0.5970 8.6699 1.0000 0.15626

11 799.0543 0.0000 8.7063 0.3271 0.03200

∑ μ1=7.841 ∑ μ2=2.3791

211















μ1 = (799.0543- 798.9951)/ 0.0618 = 0.9579

μ2 = (8.7240- 8.7223)/ 0.0541 = 0.0314

∑ μ1 + ∑ μ2 =7.841+ 2.3791 =10.22

μD = (0.9579+ 0.0314) / (10.22) = 0.09679

Multi -Objective OPF Solution-Decision Making

From the Table 5.26 (a) it is observed the μD has maximum

value in 10th row. Accordingly the corresponding values of f1 and f2

are taken as the multi objective OPF solution for the objectives

minimum fuel cost and minimum power loss respectively.




212


Objective-3 Case-2





former method.

5.3 SIMULATION RESULTS - IEEE 57 BUS TEST SYSTEM




single line diagram is shown in Fig. 5.4. The total load demand of the

system is 259MW and 7-Generators should share load optimally. The

values of fuel cost coefficients are given in Table 5.27. Generator

active power limits are presented in Table 5.28. Table 5.29 provides

Parameter values of Genetic Algorithm.



PG1 (MW) 152.23 VG1 1.016

PG2 (MW) 59.10 VG2 1.001

PG5 (MW) 24.17 VG3 1.020

PG8(MW) 30.62 VG6 1.010

PG11 (MW) 15.70 VG8 1.010

PG13 (MW) 13.23 VG9 1.000


799.0171 Power loss (MW)

8.6699




i ($/h) i ($/MWhr) i ($/MWhr2)

1 1 0 20 0.0775

2 2 0 40 0.01

3 3 0 20 0.25

4 6 0 40 0.01

5 8 0 20 0.0222

6 9 0 40 0.01

7 12 0 20 0.022

213


Testing of GSHDC-IP Algorithm for OPF Solution using suboptimal

solution obtained by Interior Point Method-Minimum Fuel Cost.




suboptimal solution by GSHDC-IP Algorithm. Finally with the help of

a well defined fitness function genetic search is carried out to find the





generation and CPU time for the minimum cost objective.


Sl.No Generator at bus # PGiMn (MW) PGiMax(MW)

1 1 0 577.88

2 2 0 100

3 3 0 140

4 6 0 100

5 8 0 350

6 9 0 100

7 12 0 410




214

Fig: 5.4 IEEE 57 – Bus Test System [101]

215





superior.


generator buses are improved in GSHDC-IP method. Also, the power

loss in transmission system is found to be less as compared to IP

method.


Testing of GSHDC-IP Algorithm for OPF Solution using suboptimal

solution obtained by Interior Point Method-Minimum Power loss

Parameter IP Method GSHDC -IP Method

PG1 (MW) 146.63 144.89

PG2 (MW) 97.79 93.08

PG3 (MW) 47.07 45.19

PG6 (MW) 72.86 68.15

PG8 (MW) 489.80 476.03

PG9 (MW) 97.63 95.90

PG12 (MW) 361.52 365.97


42,737.79 $/h 41,873.00 $/h

CPU execution time 3.17 sec 2.89 sec


Test-1 Objective-1 Case-3 (Generator Bus Voltage

Magnitude, power loss)

Parameter Suboptimal OPF solution by IP Method GSHDC-IP Method

VG1 1.040 1.050

VG2 1.008 1.010

VG3 0.985 1.003

VG6 0.980 1.026

VG8 1.044 1.050

VG9 0.980 1.044

VG12 0.992 1.015

Power loss (MW) 18.0692 17.4038

216















superior.


Test-1 Objective-2 Case-3 (Generation Schedule, cost,

CPU time)

Parameter IP Method GSHDC-IP Method

PG1 (MW) 142.63 144.78

PG2 (MW) 87.79 92.83

PG3 (MW) 45.07 45.29

PG6 (MW) 72.86 68.11

PG8 (MW) 459.80 457.30

PG9 (MW) 97.63 95.62

PG12 (MW) 361.52 366.27

Total Cost of Generation 42,354.90 $/h 41,956 $/h


217


generator buses are improved in GSHDC-IP method. Also, the power

loss in transmission system is found to be less as compared to IP










using IP method. Table 5.34 provides weightage factors and member

ship function values of the non-dominant OPF solutions which are the

core points of each of high density clusters.

Table 5.33 OPF Solution for IEEE 57-Bus System Test-1

Objective-2 Case-3 (Generator Bus Voltage Magnitude,

power loss)


GSHDC-IP Method

VG1 1.009 1.04

VG2 1.008 1.01

VG3 1.003 0.985

VG6 1.026 0.980

VG8 1.044 1.005

VG9 1.044 0.980

VG12 0.992 1.015

power loss (MW) 17.116 16.998

218


Objective-3 Case-3

f1,max=41,907.00 f1,min = 41,873.00 f2,max = 17.4038 f2,min = 16.9980




μ1 = (41,907.00- 41,874.00)/ 34.00 = 0.9705

μ2 = (17.4038- 17.3735)/ 0.4058= 0.07466

μD = (0.9705+ 0.07466) / (6.6172+ 4.92006) = 0.090589


From the Table 5.34, it is observed the μD has maximum

value in 4th row. Accordingly the corresponding values of f1 and f2 are

taken as the multi objective OPF solution for the objectives minimum

fuel cost and minimum power loss respectively.


f1 - Minimum Fuel Cost: 41,877.00 $/h.

f2 - Minimum Power Loss- 17.2410 MW.


Sl. No.


generation cost


value

Total Power loss

Membership function value

Decision making

f1 μ1 f2 μ2 μD

01 41,873.00 1.0000 17.3512 0.12962 0.097900

02 41,874.00 0.9705 17.3735 0.07466 0.090589

03 41,876.00 0.9117 17.4038 0.00000 0.079020

04 41,877.00 0.8823 17.2410 0.40118 0.111246

05 41,881.00 0.7647 17.2827 0.29842 0.092146

06 41,883.00 0.7058 17.29461 0.26909 0.084499

07 41,885.00 0.6470 17.1231 0.69172 0.116034

08 41,889.00 0.5294 17.1686 0.57959 0.096122

09 41,903.00 0.1176 17.1871 0.53400 0.056477

10 41,90400 0.0882 16.9980 1.00000 0.094320

11 41,907.00 0.0000 17.0183 0.94997 0.082339

∑ μ1=6.6172 ∑ μ2=4.92006

219

Table 5.34 (b) provi2des generation schedule, cost of generation

and CPU time, bus voltage magnitudes for the MOGA-IP OPF solution

for IEEE 57- Bus System.


Objective-3 Case-3


Testing of GSHDC-PSO Algorithm for OPF Solution using

suboptimal solution obtained by Particle Swarm Optimization Method




suboptimal solution by GSHDC-PSO Algorithm. Finally with the help

of a well defined fitness function genetic search is carried out to find

the optimal solution. The results are furnished for the objective

namely, minimum cost. The test results include the total cost of

generation, generation schedule, generator bus voltage magnitudes

and CPU execution time. Table 5.35 provides generation schedule,

cost of generation and CPU time for the min. fuel cost objective. Table

5.36 provides bus voltage magnitudes for the min. fuel cost objective.

Parameter MOGA-IP OPF Result Parameter MOGA- IP OPF Result

PG1 (MW) 145.00 VG1 1.04

PG2 (MW) 93.25 VG2 1.005

PG3 (MW) 46.45 VG3 1.001

PG6 (MW) 69.25 VG6 1.001

PG8 (MW) 461.34 VG8 1.004

PG9 (MW) 96.62 VG9 1.0032

PG12 (MW) 367.85 VG12 1.016


41,877.00 $/h Power loss (MW)

17.2410


220


execution time in GSHDC-PSO method as compared to PSO method

are superior.


Test-2 Objective-1 Case-3 (Generator Bus Voltage Magnitude,

power loss)





Testing of GSHDC-PSO Algorithm for OPF Solution using

suboptimal solution obtained by Particle Swarm Optimization Method -

Minimum Power loss.



Parameter PSO Method GSHDC-PSO Method

PG1 (MW) 145.43 140.24

PG2 (MW) 95.56 81.60

PG3 (MW) 46.12 48.32

PG6 (MW) 69.78 68.72

PG8 (MW) 479.80 476.83

PG9 (MW) 96.63 84.05

PG12 (MW) 363.52 367.69

Total Cost of Generation 42,145.79 $/h 41,327.00 $/h

CPU execution time 3.45 sec 2.98 se


GSHDC-PSO Method

VG1 1.002 1.050

VG2 1.009 1.015

VG3 0.995 1.025

VG6 0.995 1.030

VG8 1.046 1.050

VG9 0.980 1.050

VG12 1.000 1.030

Power loss (MW) 17.956 16.4471

221


minimum power loss is obtained by using PSO method. Taking this

as suboptimal solution, a high density cluster for minimum power loss

in the vicinity of suboptimal solution is formed. Finally with the help

of a well defined fitness function for minimum power loss, a genetic









execution time in GSHDC method as compared to PSO method are

superior.


Objective-2 Case-3 (Generation Schedule, cost, CPU time)

Parameter PSO Method GSHDC-PSO Method

PG1 (MW) 140.43 140.24

PG2 (MW) 85.55 81.60

PG3 (MW) 47.12 48.32

PG6 (MW) 70.70 68.72

PG8 (MW) 460.80 476.83

PG9 (MW) 97.65 84.05

PG12 (MW) 360.77 367.69

Total Cost of Generation 42,244.79 $/h 41,346.00 $/h


222




generator buses are improved in GSHDC-PSO method. Also, the power

loss in transmission system is found to be less as compared to PSO






minimum fuel cost and minimum Power loss.







Parameter Suboptimal OPF solution by PSO

Method GSHDC-PSO

Method

VG1 1.009 1.009

VG2 1.008 1.008

VG3 1.003 1.003

VG6 1.026 1.026

VG8 1.044 1.044

VG9 1.044 1.044

VG12 0.992 0.992

Power loss (MW) 17.0692 16.0692

223


Objective-3 Case-3

f1,max=41,349.00 f1,min = 41,327.00 f2,max = 16.6601 f2,min = 16.0692

f1,max - f1,min = 22.00

f2,max - f2,min = 0.5909



μ1 = (41,349.00- 41,328.00)/ 22.00 = 0.9545

μ2 = (16.6601- 16.0692)/ 0.5909= 0.17363

μD = (0.9545+ 0.17363) / (5.7268+ 4.4531) = 0.11081


From the Table 5.39(a), it is observed the μD has maximum

value in 1st row. Accordingly the corresponding values of f1 and f2 are

taken as the multi objective OPF solution for the objectives minimum

fuel cost and minimum power loss respectively.


f1 -Minimum Fuel Cost: 41,327.00 $/h.



Sl. No.


generation cost


value

Total Power loss

Member ship function value.

Decision making

f1 μ1 f2 μ2 μD

01 41,327.00 1.0 16.5312 0.21814 0.11966

02 41,328.00 0.9545 16.5575 0.17363 0.11081

03 41,330.00 0.8636 16.6601 0.0 0.08483

04 41,331.00 0.8181 16.5010 0.26925 0.10681

05 41,335.00 0.6363 16.5027 0.26637 0.08671

06 41,338.00 0.5000 16.5261 0.22677 0.07139

07 41,340.00 0.4090 16.4471 0.36046 0.07558

08 41,342.00 0.3181 16.2431 0.6041 0.09059

09 41,346.00 0.1363 16.2886 0.6287 0.07514

10 41,347.00 0.0909 16.0692 1.0 0.10716

11 41,349.00 0.0 16.1183 0.7057 0.06932

∑ μ1=5.7268 ∑ μ2=4.4531

224



solution for IEEE 57 Bus System.


Objective-3 Case-3





former method.

5.4 SUMMARY OF RESULTS

GSHDC Method is implemented for two Test cases:

Test-1: Suboptimal Solution obtained through IP method

Test-2: Suboptimal Solution obtained through PSO method

Suboptimal solution is obtained for two individual objectives

and Multi-objective:

Objective-1: Minimum Fuel Cost

Objective-2: Minimum Power Loss

Objective-3: Multi-Objective



PG1 (MW) 141.43 VG1 1.009

PG2 (MW) 87.55 VG2 1.009

PG3 (MW) 47.12 VG3 1.004

PG6 (MW) 69.43 VG6 1.028

PG8 (MW) 462.85 VG8 1.044

PG9 (MW) 98.45 VG9 1.044

PG12 (MW) 362.65 VG12 0.992


41,327.00 Power loss (MW)

16.5312


225

GSHDC is implemented for each Test case and each objective for

three case studies that is, three IEEE Test systems.




Simulation results for all the Test cases, Objectives as well as

for different case studies is furnished in earlier sections. This section

presents summary of all results obtained.

Table 5.40 presents summary of GSHDC results for the case 14

bus system.

Table 5.40: Summary of Results –Case-1: IEEE 14 - Bus System


bus system.

Table 5.41 Summary of Results–Case-2: IEEE 30 - Bus System

.

Parameter IP Method

GSHDC-IP Method

PSO Method

GSHDC-PSO Method

MOGA- GSHDC (IP Based)

MOGA- GSHDC (PSO Based)

Fuel Cost ($/h) Objective-1

8081.53 8043.30 8079.40 8038.80 8046.35 8044.35

Power Loss (MW) Objective-2

9.2469 9.1643 9.2567 9.1587 9.190 9.180

Parameter IP Method

GSHDC-IP Method

PSO Method

GSHDC-PSO Method

MOGA- GSHDC (IP Based)

MOGA- GSHDC (PSO Based)

Fuel Cost ($/h) Objective-1

810.61 806.7008 807.961 798.9925 806.7135 799.0171

Power Loss (MW) Objective-2

10.830 10.558 10.47 8.6699 10.6296 8.6699

226


bus system.

Table 5.42 Summary of Results –Case-3: 57 - Bus System

When compared to GSHDC-IP, the results of GSHDC-PSO are better in

all the three cases. Though, GSHDC-PSO is giving best results, for the

single objective of minimum fuel cost and the single objective of

minimum losses, individually, the MOGA-GSHDC (PSO based) is

giving a better compromised OPF solution including both fuel cost

and losses.

5.5 OPF SIMULATION RESULTS - IEEE 14 BUS TEST SYSTEM-

MODIFIED PENALTY FACTOR METHOD

In addition to suboptimal solutions obtained through IP and

PSO methods, a modified penalty factor method presented in Section

5.4 is used to obtain suboptimal solution or a core point in High

Density Cluster. This section presents results for this case.

The GSHDC -penalty factor performance is evaluated on the

standard IEEE 30-bus test system [27]. The system consists of 41-

lines, 6-generators, 4-Tap-hanging transformers and shunt capacitor

banks located at 9-buses. The test is carried with a 1.4-GHz Pentium-

IV PC. The GSHDC -penalty factor has been developed by the use of

Parameter IP Method

GSHDC-IP Method

PSO Method

GSHDC-PSO

Method

MOGA- GSHDC

(IP Based)

MOGA- GSHDC

(PSO Based)

Fuel Cost ($/h)

42,739.79 41,873.00 42,145.79 41,327.00 41,877.00 41327.00

Power Loss (MW)

17.116 16.998 17.0692 16.0692 17.2410 16.5312

227

MATLAB version 7. The parameter settings to execute GSHDC-penalty

factor are probability of crossover=0.5, probability of Mutation= 0.7,

the population size is 20. The study is carried out for a total system

load of 283.4 MW. The power mismatch tolerance is 0.0001 p.u. and

other parameters are presented in Table 5.43.

Table 5.43: Test-3 Objective-1 Case 2

Power Generation Limits and Generator cost parameters of IEEE

30 Bus System (Base MVA 100)

Table-5.44 Test-3 Objective-1 Case 2

Test results of GSHDC-penalty factor and EGA method [103]

The performance of GSHDC is -penalty factor compared with the

results of EGA [103] method and is tabulated in Table-5.44. For a

given system load, the total generation in the system by GSHDC-

penalty factor method is found slightly higher compared to that of EGA

Bus Pmin Pmax Qmin Qmax

1 0.5 2 -0.2 2 0 200 37.5

2 0.2 0.8 -0.2 1 0 175 175

5 0.15 0.5 -0.15 0.8 0 100 625

8 0.1 0.35 -0.15 0.6 0 325 83.4

11 0.1 0.3 -0.1 0.5 0 300 250

13 0.12 0.4 -0.15 0.6 0 300 250

GEN. NO

BUS NO

BUS VOLTAGES ACTIVE POWER GENERATION

COST OF GENERATION

EGA [103]

GSHDC-penalty factor

EGA [103]


EGA [103]


1 1 1.050 1.0600 176.20

177.216 468.84 468.3056

2 2 1.038 1.0430 48.75 48.3660 126.89 127.3034

3 5 1.012 1.0100 21.44 21.203 50.19 49.3009

4 8 1.020 1.0100 21.95 21.977 75.35 77.2442

5 11 1.087 1.082 12.42 12.182 41.13 40.6177

6 13 1.067 1.0710 12.02 12.00 39.67 39.600

TOTAL 292.79 292.944 802.06 802.3709

228

[103] method. The % high values are presented in Table-5.45. The

numerical difference can be ignored. The EGA [103] for an IEEE30-

Bus system is carried out with a computer having the same

configuration as mentioned above. Now, the comparison is made in

terms of generation cost and CPU time. The GSHDC -penalty factor

method gave less cost of generation. The GSHDC-penalty factor

method has completed objective-1 study in 8 seconds and objective-1

and objective -2 together in 12 seconds in contrast to 85 seconds that

is taken by EGA method. The authors of EGA method in their

conclusions have mentioned the high execution time of their method.

This proves the GSHDC-penalty factor method is quite acceptable for

large size power systems and for on-line studies.

Table-5.45: Test-3 Objective-1 & Objective-2 Case 2

Generation Schedule of GSHDC-penalty factor Compared to EGA [103]

Method

Total Active Power Generation Objective-1

Transmission Losses Objective-2

Total cost CPU Time

MW

%H

igh

com

pare

d t

o

EG

A m

eth

od

MW

%H

igh

com

pare

d t

o

EG

A m

eth

od

$/h

%H

igh

com

pare

d t

o

EG

A m

eth

od

Sec

EGA[103] 292.79 ---- 9.39 ---- 802.06 ---- 85

GSHDC-penalty factor ( Objective-1 Total fuel Cost minimum)

292.94 0.028 9.54 0.84 802.370 0.038 8

GSHDC-penalty factor Objective-2 (Total loss minimum)

292.78 ----- 9.38 ------ 802.510 12

229

Next, the performance of GSHDC-penalty factor is compared with the

other methods and is tabulated in Table-5.46. For a given system

load and total generation, the results of GSHDC -penalty factor

method is found better as compared to other existing methods.

However, Test-1 (sub optimal solution by IP method) and Test-2 (sub

optimal solution by PSO method) are much superior. Hence, Test-3

case (sub optimal solution by modified penalty factor method) is not

considered and not studied for other case studies like 14, and 57 bus

systems.

Table-5.46 Test-3 Objective-1 & Objective-2 Case 2

Generation Schedule of GSHDC-penalty factor Compared with

Evolutionary methods

5.6 COMPARISON OF GSHDC-IP & GSHDC-PSO OPF RSULTS

WITH OTHER METHODS.

The simulation results of GSHDC-IP (with suboptimal solution

obtained through IP) method and GSHDC-PSO (with suboptimal

solution obtained through PSO) method have been presented in

earlier sections for two objectives (minimum fuel cost and minimum

power loss) and multi-objective for different case studies 14,30, and

OPF Method Total Active Power Generation in MW

Transmission Losses in MW

Total cost in $/h

CPU Time in Sec


292.8722 9.47 802.3709 8

EGA[103] 292.79 9.39 802.06 85

GAOPF[26] L.Lai

293.0372 9.6372 802.4484 315

EPOPF[25] Yuryevich

292.7682 9.3683 802.62 51.4

230

57 bus systems. It can be observed, if single objective is the criteria,

GSHDC-PSO gives the best results. However, simulation results

indicate the multi-objective results are not far deviating from the best

results obtained from the single objective case studies.

This section presents comparative results of GSHDC-PSO with

the existing methodologies. A typical case study of IEEE 30-Bus

system is taken for the performance evaluation of the proposed

GSHDC-PSO. The comparison results are presented in Table 5.47.

Table-5.47 COMPARISON OF GSHDC-PSO OPF RESULTS WITH

OTHER METHODS.

As seen in Table 5.47, the results of GSHDC-PSO method are

found better as compared to other existing methods. Further, the

results obtained through MOGA-GSHDC (PSO based) are comparable

with those of GSHDC-PSO and better than other methods. Losses as

well as CPU time using GSHDC-PSO are much improved. Though the

single objective (of minimum fuel cost) GSHDC-PSO is giving best

minimum fuel cost, but the MOGA-GSHDC (PSO based) is giving a

better compromised OPF solution between losses and cost.

OPF Method

Total Active Power Generation in MW

Transmission Losses in MW

Total cost in $/h

CPU Time in Sec

GSHDC-PSO 292.12 8.7190 798.9925 2.54

MOGA-GSHDC (PSO based)

292.12 8.7185 799.0021 8.475

EGA[103] 292.79 9.39 802.06 85

IGAOPF[102] L.Lai 292.54 9.14 800.805 315

EPOPF[25] Yuryevich 292.7682 9.3683 802.62 51.4

AGA[105] Liladhur.G 297.45 14.05 801.17 433

231

5.7 CONCLUSIONS

A novel method for the solution of Optimal Power Flow is

proposed in this chapter. The limitations of analytical and intelligent

methods have been overcome by the proposed methods namely,

GSHDC-IP Method, GSHDC-PSO Method, MOGA-GSHDC (IP based)

and MOGA-GSHDC (PSO based).

In this chapter, testing of GSHDC-IP Algorithm, for OPF problem

using suboptimal solution obtained by Interior Point Method is carried

out to obtain solution individually for minimum fuel cost and

minimum power loss. In addition testing of MOGA-GSHDC (IP based)

Algorithm has been carried out to obtain multi objective solution

simultaneously for minimum fuel cost and minimum power loss. The

testing of these Algorithms has been done for the well-known standard

IEEE test cases such as 14-bus system, 30-bus system and 57-bus

system.

Similarly, testing of GSHDC-PSO Algorithm for OPF problem

using suboptimal solution obtained by PSO Method is carried out to

obtain solution individually for minimum fuel cost and minimum

power loss. In addition testing of MOGA-GSHDC (IP based) Algorithm

has been carried out to obtain multi objective solution simultaneously

for minimum fuel cost and minimum power loss.

When compared to GSHDC-IP, the results of GSHDC-PSO are

better in all the three cases. Though, GSHDC-PSO is giving best

results, for the single objective of minimum fuel cost and the single

objective of minimum losses, individually, the MOGA-GSHDC (PSO

232

based) is giving a better compromised OPF solution including both

fuel cost and losses.

Further, results of GSHDC-PSO are compared with the existing

methodologies. A typical case study of IEEE 30-Bus system is taken

for the performance evaluation of the proposed GSHDC-PSO. The

results of GSHDC-PSO method are found better as compared to other

existing methods. Further, the results obtained through MOGA-

GSHDC (PSO based) are comparable with those of GSHDC-PSO and

better than other methods. Losses as well as CPU time using GSHDC-

PSO are much improved. Though the single objective (of minimum

fuel cost) GSHDC-PSO is giving best minimum fuel cost, but the

MOGA-GSHDC (PSO based) is giving a better compromised OPF

solution between losses and cost.

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CHAPTER 5 SIMULATION RESULTS & DISCUSSION …shodhganga.inflibnet.ac.in/bitstream/10603/4566/15/15_chapter 5.pdf · CHAPTER – 5 SIMULATION RESULTS & DISCUSSION 5.0 INTRODUCTION